Hi Christian, four different possibilities come into my mind. You already mentioned most of them:
[b]3D View[/b]
You may use the Planes Panel for clipping/carving. After that, use the Navigation Panel which enables you to enter the perspective from where you are looking. In this regard, you do not have to use the mouse for navigation.
[b]Exporting heads to a shapefile (manual way)[/b]
That's a possible "dirty" way: If the nodes located on your different slices are vertically located at the elevation of interest for the horizontal section and if the horizontal population of the nodes are dense enough you can create a selection. Use the selection and export the heads from the Data Panel into a point-shapefile.
[b]Exporting heads to a shapefile (automatic way)[/b]
You may use the FEFLOW API. Retrieve all nodal X, Y, Z and head values and store them in an array. After that, loop vertically through the nodes located at the different slices starting from the first slice. Within the loop, you may retrieve nodal elevations using [font=courier][color=blue]IfmGetZ(nNode)[/color][/font]. If the upper node is greater than the elevation of interest (for the horizontal section) AND if the lower node is smaller than the elevation of interest, then you have to remember the heads computed from FEFLOW at the two nodes. Based on the elevations and heads of the upper and lower nodes and your additional elevation of interest, you can make a simple vertical 1D interpolation. As a result you have the head at the elevation of interest. If you do that for each XY-position (=[font=courier][color=blue]IfmGetNumberOfNodesPerSlice[/color])[/font], then you have all nodal elevations which are required for the horizontal section.
If you use the Python API and if you use a GIS which supports Python (e.g. ArcGIS => [font=courier][color=blue]arcpy[/color][/font],QGIS =>[font=courier][color=blue]PyQGIS[/color][/font]) you can generate a single pipeline. After you finished the steps as described above you can write a point-shapefile, fill the attribute table with the values for X, Y and heads. Use these columns to generate a TIN. Of course you can also do the GIS steps manually.
If you use ArcGIS the following functions can be usefull (without having the warranty of completeness):
[font=courier][color=blue]
arcpy.AddField_management()
arcpy.CalculateField_management()
arcpy.CreateTin_3d()
arcpy.AddSurfaceInformation_3d()
arcpy.Point()
arcpy.PointGeometry()
[/color][/font]
[b]Write a VTK file[/b]
You may write a VTK file by using the FEFLOW API and use the Clip filter ParaView.